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Study Guides > College Algebra

Solutions

Solutions to Try Its

1. [latex]x=-5[/latex] 2. [latex]x=-3[/latex] 3. [latex]x=\frac{10}{3}[/latex] 4. [latex]x=1[/latex] 5. [latex]x=-\frac{7}{17}[/latex]. Excluded values are [latex]x=-\frac{1}{2}[/latex] and [latex]x=-\frac{1}{3}[/latex]. 6. [latex]x=\frac{1}{3}[/latex] 7. [latex]m=-\frac{2}{3}[/latex] 8. [latex]y=4x - 3[/latex] 9. [latex]x+3y=2[/latex] 10. Horizontal line: [latex]y=2[/latex] 11. Parallel lines: equations are written in slope-intercept form. Coordinate plane with the x-axis ranging from negative 5 to 5 and the y-axis ranging from negative 1 to 6. Two functions are graphed on the same plot: y = x/2 plus 5 and y = x/2 plus 2. The lines do not cross. 12. [latex]y=5x+3[/latex]

Solutions to Odd-Numbered Exercises

1. It means they have the same slope. 3. The exponent of the [latex]x[/latex] variable is 1. It is called a first-degree equation. 5. If we insert either value into the equation, they make an expression in the equation undefined (zero in the denominator). 7. [latex]x=2[/latex] 9. [latex]x=\frac{2}{7}[/latex] 11. [latex]x=6[/latex] 13. [latex]x=3[/latex] 15. [latex]x=-14[/latex] 17. [latex]x\ne -4[/latex]; [latex]x=-3[/latex] 19. [latex]x\ne 1[/latex]; when we solve this we get [latex]x=1[/latex], which is excluded, therefore NO solution 21. [latex]x\ne 0[/latex]; [latex]x=\frac{-5}{2}[/latex] 23. [latex]y=\frac{-4}{5}x+\frac{14}{5}[/latex] 25. [latex]y=\frac{-3}{4}x+2[/latex] 27. [latex]y=\frac{1}{2}x+\frac{5}{2}[/latex] 29. [latex]y=-3x - 5[/latex] 31. [latex]y=7[/latex] 33. [latex]y=-4[/latex] 35. [latex]8x+5y=7[/latex] 37. Parallel Coordinate plane with the x and y axes ranging from negative 10 to 10. The functions 3 times x minus 2 times y = 5 and 6 times y minus 9 times x = 6 are graphed on the same plot. The lines do not cross. 39. Perpendicular Coordinate plane with the x and y axes ranging from negative 10 to 10. The function y = negative 3 and the line x = 4 are graphed on the same plot. These lines cross at a 90 degree angle. 41. [latex]m=\frac{-9}{7}[/latex] 43. [latex]m=\frac{3}{2}[/latex] 45. [latex]{m}_{1}=\frac{-1}{3},\text{ }{m}_{2}=3;\text{ }\text{Perpendicular}[/latex] 47. [latex]y=0.245x - 45.662[/latex]. Answers may vary. [latex]{y}_{\text{min}}=-50,\text{ }{y}_{\text{max}}=-40[/latex] 49. [latex]y=-2.333x+6.667[/latex]. Answers may vary. [latex]{y}_{\mathrm{min}}=-10, {y}_{\mathrm{max}}=10[/latex] 51. [latex]y=\frac{-A}{B}x+\frac{C}{B}[/latex] 53. Yes, they are perpendicular.
[latex]\begin{array}{l}\text{The slope for }\left(-1,1\right)\text{ to }\left(0,4\right)\text{ is }3.\\ \text{The slope for }\left(-1,1\right)\text{ to }\left(2,0\right)\text{ is }\frac{-1}{3}.\\ \text{The slope for }\left(2,0\right)\text{ to }\left(3,3\right)\text{ is }3.\\ \text{The slope for }\left(0,4\right)\text{ to }\left(3,3\right)\text{ is }\frac{-1}{3}\end{array}[/latex].
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